Whitham hierarchies, instanton corrections and soft supersymmetry breaking in N = 2 SU(N) super Yang-Mills theory

We study N = 2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated with the root lattice of the group. Explicit results for the one- and two-instanton corrections in SU(N) are presented. interpreting the slow times of the hierarchy as additional couplings, we show how they can be promoted to spurion superfields that softly break N = 2 supersymmetry down to N = 0. This provides a family of non-supersymmetric deformations of the theory, associated with higher Casimir operators of the gauge group. The SU(3) theory is analyzed in some detail. (C) 1999 Elsevier Science B.V.